Determine the force-memory time

Determine the memory time of the hereditary induced-wake force for binaries in stochastic scalar backgrounds, and establish whether the force becomes insensitive to earlier orbital motion after a few orbital periods.

Background

The paper assumes that the force memory time is of order a few orbital periods in order to replace the stochastic background by the density of the local quasi-static patch. This assumption is important for deriving the order-unity realization-dependent fluctuations in cases 3, 4, and 8.

Because the force is hereditary and may retain nonlocal dependence on the orbital history, an explicit determination of the memory time is needed to justify the local-density approximation and its associated flux correlation function.

References

We do not calculate $t_{\rm mem}$ in this work. Instead, we make the working assumption $t_{\rm mem}={\rm few}\times\mathcal O(T)$, so that the force becomes insensitive to the earlier motion after a few orbital periods. This assumption is well-motivated by the finite-time calculations by Buehler and Desjacques, but we have not explicitly established it in this work.

— Dynamical Friction in an Ultralight Scalar Medium across Coherent and Stochastic Regimes  (2609.28641 - Mitra et al., 23 Sep 2026) in Section 5.2.1, subsection “One quasi-static patch: cases 3, 4, and 8”